Cyclists are supposed to ride the same direction as the traffic. Yes, that does mean that cyclists do not see vehicles coming and may have less warning in the event of an accident. However, riding against traffic, even though you can see, is far more dangerous.
For one thing, it massively increases the overall speed of the crash. This is known as the closing speed. For instance, imagine that you're riding your bike at 15 mph. Traffic is going the same direction you are at 30 mph. If you are hit, the overall closing speed of the initial crash is just 15 mph.
If you're going toward the car that hits you, though, you have to add the two speeds together, giving you a total crash speed of 45 mph -- three times as fast.
On top of that, your reaction times are far lower when you're going toward the other vehicles, thanks to the closing speed increase. The driver's reaction time is also far less. A car may drift into the bike lane for a second. If the car is behind you, the driver has time to correct before he or she hits you. If the car is ahead of you, coming toward you, the driver can't correct in time and plows into your bike.
You also have to factor in driver expectations. A driver doesn't expect you to be going the wrong way. For instance, a driver who is turning right is going to check to his or her left at the intersection. If you're coming from the right, he or she may never see you before pulling out in front of you.
As you can see, following bike laws does help to keep you safe. That said, it can't prevent all accidents, which are often caused by negligent drivers, so it's important to know your legal rights when you follow the law and are still hit and injured.
Source: Antranik, "How To Ride Your Bicycle Safely On The Street," accessed Oct. 20, 2017